.TH std::ranges::push_heap 3 "2024.06.10" "http://cppreference.com" "C++ Standard Libary"
.SH NAME
std::ranges::push_heap \- std::ranges::push_heap

.SH Synopsis
   Defined in header <algorithm>
   Call signature
   template< std::random_access_iterator I, std::sentinel_for<I> S,

             class Comp = ranges::less, class Proj = std::identity >
   requires std::sortable<I, Comp, Proj>                              \fB(1)\fP \fI(since C++20)\fP
   constexpr I

       push_heap( I first, S last, Comp comp = {}, Proj proj = {} );
   template< ranges::random_access_range R, class Comp =
   ranges::less,

             class Proj = std::identity >                             \fB(2)\fP \fI(since C++20)\fP
   requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
   constexpr ranges::borrowed_iterator_t<R>

       push_heap( R&& r, Comp comp = {}, Proj proj = {} );

   Inserts the element at the position last - 1 into the max heap defined by the range
   [first, last - 1).

   1) Elements are compared using the given binary comparison function comp and
   projection object proj.
   2) Same as \fB(1)\fP, but uses r as the range, as if using ranges::begin(r) as first and
   ranges::end(r) as last.

   The function-like entities described on this page are niebloids, that is:

     * Explicit template argument lists cannot be specified when calling any of them.
     * None of them are visible to argument-dependent lookup.
     * When any of them are found by normal unqualified lookup as the name to the left
       of the function-call operator, argument-dependent lookup is inhibited.

   In practice, they may be implemented as function objects, or with special compiler
   extensions.

.SH Parameters

   first, last - the range of elements defining the heap to modify
   r           - the range of elements defining the heap to modify
   pred        - predicate to apply to the projected elements
   proj        - projection to apply to the elements

.SH Return value

   An iterator equal to last.

.SH Complexity

   Given N = ranges::distance(first, last), at most \\(\\scriptsize \\log{(N)}\\)log(N)
   comparisons and \\(\\scriptsize 2\\log{(N)}\\)2log(N) projections.

.SH Notes

   A max heap is a range of elements [f, l), arranged with respect to comparator comp
   and projection proj, that has the following properties:

     * With N = l - f, p = f[(i - 1) / 2], and q = f[i], for all 0 < i < N, the
       expression std::invoke(comp, std::invoke(proj, p), std::invoke(proj, q))
       evaluates to false.
     * A new element can be added using ranges::push_heap, in \\(\\scriptsize
       \\mathcal{O}(\\log N)\\)𝓞(log N) time.
     * The first element can be removed using ranges::pop_heap, in \\(\\scriptsize
       \\mathcal{O}(\\log N)\\)𝓞(log N) time.

.SH Possible implementation

struct push_heap_fn
{
    template<std::random_access_iterator I, std::sentinel_for<I> S,
             class Comp = ranges::less, class Proj = std::identity>
    requires std::sortable<I, Comp, Proj>
    constexpr I
        operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
    {
        const auto n{ranges::distance(first, last)};
        const auto length{n};
        if (n > 1)
        {
            I last{first + n};
            n = (n - 2) / 2;
            I i{first + n};
            if (std::invoke(comp, std::invoke(proj, *i), std::invoke(proj, *--last)))
            {
                std::iter_value_t<I> v {ranges::iter_move(last)};
                do
                {
                    *last = ranges::iter_move(i);
                    last = i;
                    if (n == 0)
                        break;
                    n = (n - 1) / 2;
                    i = first + n;
                }
                while (std::invoke(comp, std::invoke(proj, *i), std::invoke(proj, v)));
                *last = std::move(v);
            }
        }
        return first + length;
    }

    template<ranges::random_access_range R, class Comp = ranges::less,
             class Proj = std::identity>
    requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
    constexpr ranges::borrowed_iterator_t<R>
        operator()(R&& r, Comp comp = {}, Proj proj = {}) const
    {
        return (*this)(ranges::begin(r), ranges::end(r), std::move(comp), std::move(proj));
    }
};

inline constexpr push_heap_fn push_heap {};

.SH Example


// Run this code

 #include <algorithm>
 #include <cmath>
 #include <iostream>
 #include <vector>

 void out(const auto& what, int n = 1)
 {
     while (n-- > 0)
         std::cout << what;
 }

 void print(auto rem, auto const& v)
 {
     out(rem);
     for (auto e : v)
         out(e), out(' ');
     out('\\n');
 }

 void draw_heap(auto const& v)
 {
     auto bails = [](int n, int w)
     {
         auto b = [](int w) { out("┌"), out("─", w), out("┴"), out("─", w), out("┐"); };
         if (!(n /= 2))
             return;
         for (out(' ', w); n-- > 0;)
             b(w), out(' ', w + w + 1);
         out('\\n');
     };
     auto data = [](int n, int w, auto& first, auto last)
     {
         for (out(' ', w); n-- > 0 && first != last; ++first)
             out(*first), out(' ', w + w + 1);
         out('\\n');
     };
     auto tier = [&](int t, int m, auto& first, auto last)
     {
         const int n{1 << t};
         const int w{(1 << (m - t - 1)) - 1};
         bails(n, w), data(n, w, first, last);
     };
     const int m{static_cast<int>(std::ceil(std::log2(1 + v.size())))};
     auto first{v.cbegin()};
     for (int i{}; i != m; ++i)
         tier(i, m, first, v.cend());
 }

 int main()
 {
     std::vector<int> v{1, 6, 1, 8, 0, 3,};
     print("source vector v: ", v);

     std::ranges::make_heap(v);
     print("after make_heap: ", v);
     draw_heap(v);

     v.push_back(9);

     print("before push_heap: ", v);
     draw_heap(v);

     std::ranges::push_heap(v);
     print("after push_heap: ", v);
     draw_heap(v);
 }

.SH Output:

 source vector v: 1 6 1 8 0 3
 after make_heap: 8 6 3 1 0 1
    8
  ┌─┴─┐
  6   3
 ┌┴┐ ┌┴┐
 1 0 1
 before push_heap: 8 6 3 1 0 1 9
    8
  ┌─┴─┐
  6   3
 ┌┴┐ ┌┴┐
 1 0 1 9
 after push_heap: 9 6 8 1 0 1 3
    9
  ┌─┴─┐
  6   8
 ┌┴┐ ┌┴┐
 1 0 1 3

.SH See also

   ranges::is_heap       checks if the given range is a max heap
   (C++20)               (niebloid)
   ranges::is_heap_until finds the largest subrange that is a max heap
   (C++20)               (niebloid)
   ranges::make_heap     creates a max heap out of a range of elements
   (C++20)               (niebloid)
   ranges::pop_heap      removes the largest element from a max heap
   (C++20)               (niebloid)
   ranges::sort_heap     turns a max heap into a range of elements sorted in ascending
   (C++20)               order
                         (niebloid)
   push_heap             adds an element to a max heap
                         \fI(function template)\fP
